Inductive Reasoning and Scientific Practical Reasoning

Overview of Inductive Reasoning in Science and Everyday Life

Inductive reasoning is the primary method found in the sciences and everyday life. It involves the methods of scientific or empirical research, specifically how data are presented and how conclusions are drawn. The quality of reasoning in scientific or empirical claims is determined by the relationship between the evidence provided in the premises and the probability of the conclusion.

Fundamental Concepts of Inductive Arguments

An inductive argument is defined as an argument where the premises provide some good reasons or evidence to support the truth of the conclusion. In these arguments, it is possible for the premises to be true while the conclusion is false without any logical contradiction, distinguishing them from deductive arguments.

• Premises as Evidence: The premises are treated as data, evidence, observation reports, or research findings.

• Probability: The degree of probability concerning the truth of the conclusion depends on the quality and quantity of the evidence provided in the premises.

Comparative Strength of Inductive Arguments

To understand the strength of inductive reasoning, consider two examples regarding weather patterns:

• Example 1 (Strong): For the past twenty years of my life, it has been raining every Friday. Tomorrow is Friday. Therefore, it will rain tomorrow.

• Example 2 (Weak): For the past three weeks, it has been raining every Friday. Tomorrow is Friday. So, it will rain tomorrow.

Both examples are inductive because the conclusion could be false even if the premises are true. However, the evidence in Example 1 (twenty years of data) is stronger than the evidence in Example 2 (three weeks of data). Consequently, Example 1 represents strong inductive reasoning, while Example 2 represents weak inductive reasoning, as the probability of the conclusion being false is higher in the second case.

Verifiable and Confirmable Statements

Statements in inductive arguments are categorized as either verifiable or confirmable.

Verifiable Statements (Particular Statements)

Verifiable statements are also referred to as evidence, data, test results, or observation reports.

• Definition: A verifiable statement is directly testable through experience because its reference class or subject is finite (countable or fixed).

• Nature of Truth: One can attain the definitive truth of the statement by accessing every member or instance in the reference class.

• Examples:

  • Next week Friday it will rain.

  • The students in this class are from the distance education school.

  • Accra is filthy.

• Testing Method: Because the subject is finite, a test, experiment, or observation can be conducted directly (one or a few times) to establish truth or falsity.

Confirmable Statements (General Statements)

Confirmable statements are also known as hypotheses.

• Definition: A confirmable statement is indirectly testable through experience because its reference class or subject is infinite (uncountable or limitless).

• Nature of Truth: Due to the countless number of subjects, one cannot test or observe directly to fully determine whether they are true or false.

• Examples:

  • Every Friday it rains.

  • All students are from a distance education school.

  • Some taxi drivers in Accra can speak Chinese.

  • Some students cheat in exams.

  • All snakes are poisonous.

• Testing Method: These are testable indirectly based on the results of verifiable statements. For instance, even if it rains every Friday for ten years, it is impossible to exhaustively test all future Fridays. If it fails to rain on a single Friday in the eleventh year, the statement "Every Friday it rains" becomes false.

Types of Hypotheses

There are two primary types of hypotheses or confirmable statements. A statement must be a general/confirmable statement before it can be classified as law-like or statistical.

Law-like Hypotheses

A law-like hypothesis is a confirmable statement that possesses no exceptions. It attributes a property to every individual in its reference class.

• Logical Form: "All As are Bs" or "No As are Bs."

• Examples:

  • All metals expand when heated.

  • All living things require oxygen to live.

  • No student registers unless forced.

  • All voters hate the New Famous Party.

Statistical Hypotheses

A statistical hypothesis is a confirmable statement that admits exceptions.

• Logical Form: "Some As are Bs" or "Most As are not Bs."

• Indicators: Words such as "some," "occasionally," "few," "most," "many," and "typically," as well as specific percentages.

• Examples:

  • Most metals expand when heated.

  • Some students register when they are forced.

  • $80\%$ of Ghanaian voters do not like the New Member of Parliament (implying a $20\%$ exception).

  • Almost all Ghanaians are afraid of the COVID-19 virus.

Predictive Power and Falsifiability

Predictive power is the ability of a statement to provide information about the future.

Law-like Hypotheses and High Predictive Power

• Prediction: Because there are no exceptions, law-like statements provide information about all members of a class, including those in the future. For example, if "Every Friday it rains" is true, we can predict with certainty that the next Friday will be rainy.

• Falsifiability: These are more easily falsifiable. If a single instance occurs where it does not rain on a Friday, the law-like statement is proven false.

Statistical Hypotheses and Low Predictive Power

• Prediction: Because they allow for exceptions, statistical statements provide less certain information about the future. If "Most of the time, it rains on Friday" is true, one cannot say with certainty that next Friday will rain because that day could be an exception.

• Falsifiability: These are less falsifiable. If it does not rain on one Friday, the statement "Most Fridays it rains" remains true.

Enumerative Induction

Enumerative induction (or induction by enumeration) is a type of inductive argument that uses verifiable (particular) statements as premises to support a confirmable statement (hypothesis) as a conclusion.

• Process: The conclusion is reached based on an accumulated number of listed or numbered instances.

• Frequency: Enumerative induction confirms statistical hypotheses more often than law-like hypotheses.

Examples of Enumerative Induction

Scenario A: Law-like Conclusion An experiment feeds five different snakes live rats:

1. The first snake bit its rat, and the rat died.

2. The second snake bit its rat, and the rat died.

3. The third snake bit its rat, and the rat died.

4. The fourth snake bit its rat, and the rat died.

5. The fifth snake bit its rat, and the rat died. Summary: The five snakes all killed their rats after biting them. Conclusion: Therefore, ALL SNAKES ARE POISONOUS.

Scenario B: Statistical Conclusion An experiment feeds five different snakes live rats:

1. The first snake bit its rat, and the rat died.

2. The second snake bit its rat, and the rat died.

3. The third snake bit its rat, and the rat died.

4. The fourth snake bit its rat, and the rat did not die.

5. The fifth snake bit its rat, and the rat did not die. Summary: $3$ out of $5$ snakes killed their rats. Conclusion: Therefore, $60\%$ OF SNAKES ARE POISONOUS.

Uncertainty as a Virtue in Science

Absolute certainty is unattainable in inductive reasoning. Premises only confirm a conclusion to a certain degree of probability. However, this uncertainty is a primary virtue in scientific and everyday understanding.

Falsifiability and Knowledge

• Empirical Content: If a statement is falsifiable (can be doubted or tested), it provides knowledge about the world. Statements with knowledge are said to have empirical content.

• Progress: The ability to doubt or test a statement provides a reason to seek the truth, leading to new knowledge.

Illustration of Knowledge through Falsifiability

Imagine being in an enclosed room and asking someone if it is raining outside.

• Scenario 1 (Falsifiable): The person says, "It is raining outside." This is testable. If you step out and see raindrops, your knowledge is confirmed. If you step out and find the ground dry, you gain the new knowledge that it is not raining. Gaining this knowledge was possible because the original statement was falsifiable.

• Scenario 2 (Unfalsifiable): The person says, "Either it is raining outside or it is not raining." This statement is true regardless of the weather (it covers all possibilities). It provides no practical help in deciding whether to take an umbrella and offers no specific knowledge about the world because it cannot be proven false.

Summary of Falsifiable Statements

1. Any particular observation statements (falsifiable).

2. Law-like hypotheses (more or less easily falsifiable).

3. Statistical hypotheses (less falsifiable but still testable).

Uncertainty is a virtue because falsifiability is the mechanism through which knowledge of the world is acquired and refined.